1. Technical Field
The present disclosure relates to a method and a device for detecting a phase error of a received signal, and, in particular, to the reception of a signal digitally modulated by phase and possibly amplitude shifted.
2. Description of the Related Art
Most digital demodulators utilize a phase detection device allowing a reference carrier signal locally generated by the receiver to be aligned with the phase of the transmitter of these signals. Now, from the transmission thereof, a signal transmitted is subjected to various frequency translations generating a phase noise which may be relatively significant. The phase noise generally includes high frequency components and low frequency components. The low frequency components of the phase noise may be compensated by evaluating a phase error from a number of successive symbols resulting from the sampling of the received signal, corrected at least partially directly or in a phase-lock loop PLL.
If the symbols transmitted are not known in advance i.e., in the absence of pilot symbols, there is no simple means for evaluating a phase error or the phase of the received signal. However, in a phase-lock loop, a magnitude is evaluated to cancel the average value of the phase error. The magnitude may be evaluated symbol by symbol in the phase-lock loop, at least when the phase error to be evaluated is low, so as to guarantee a convergence of the loop. In practice, this magnitude consists of a periodic and odd function of the phase error and a measure noise that depends on the noise of the signal, approximations of the magnitude estimator and especially on the fact that the value of the symbols is unknown. That is why, generally, it is not desired to evaluate the absolute phase of the symbol transmitted (for example in QPSK, the error measures are modulo π/2).
Conventionally, the phase error PHE on a received symbol may be evaluated on the basis of the following formula:PHE(S)=ℑm(S·Ŝ*)  (1)    where ℑm(X) is a function giving the imaginary part of a complex number X, S represents the complex value of the received symbol and Ŝ* represents the complex conjugate value of an estimation of the symbol S. When the symbols are transmitted by a digital phase modulation having a simple constellation, such as QPSK (S=I+jQ where I and Q are equal to + or −1), the formula (1) simplifies as follows:PHE(S)=Q·sign(I)−I·sign(Q)  (2)    where sign(x) is a function equal to +1 or −1 according to the sign of the variable x.
However, the simplified formula (2) becomes ineffective if a relatively significant noise causes decision errors regarding the value of the received symbol. Thus, in the case of a QPSK modulation, if the received symbol has an imaginary part Q near 0, the phase error detected has a sign that has a 50% chance of being erroneous. In addition, the signal to be processed may be disturbed by interferences caused by a simple constant frequency carrier or by a signal having a lower power, transmitted in a same transmission channel as the signal to be processed. Such interferences may cause the phase-lock loop to diverge, even in the absence of any other noise.
According to the theory for evaluating a parameter with a maximum of likelihood, optimum phase detection in an operation of receiving symbols may be modeled as follows:
                              OPD          ⁡                      (            S            )                          =                              ∂                          ∂              θ                                ⁢                                    Ln              (                              Pr                ⁡                                  (                                      S                    ❘                    θ                                    )                                            ]                                      θ              =              0                                                          (        3        )                where Pr(S|θ) is the probability that the symbol S has a phase equal to θ, Ln is the Napierian logarithm function and
                         ∂                  ∂          θ                    ⁢      X        ]        θ    =    0      is the derivative of X in relation to θ near θ=0. In the formula (3), it appears that the function OPD( ) may be entirely determined if the noise distribution affecting the symbol in the complex plane is known.
Generally, phase detections are performed from approximations of the formula (3) based on a modeling of the average noise distribution. According to this evaluation and modeling complexity, the result is a more or less simple detection function. In some cases, the detection function is performed using look-up tables LUT depending on noise, addressed by the components I and Q of the received symbol. These tables are stored in a memory of a ROM or a RAM type if the values of the tables must be recalculated to take into account the evolution of noise distribution. Currently, the best phase detections use look-up tables that usually have 16 000 values, even using a rotational symmetry appearing in the noise distribution in the complex plane. The implementation of such tables therefore requires a not negligible calculation and loading time, and a relatively significant space in memory.
In the case of a noise caused by interference with a signal near in frequency, the interference noise alternately passes between a state in phase and a state out of phase with the received signal. The result is that the look-up table must be frequently recalculated, which may be impossible for current symbol rates, around 20 to 30 MBauds. It may then be considered to determine a compromise supplying a result acceptable for any case.